Tangent Meets Chord
Part of the Circles section of Coddy's Geometry journey. Lesson 53 of 62.
A circle chase links the rules of this section one after another. The trick is to ask, at each step, what the angle you just found unlocks. Radii make isosceles triangles, tangents make right angles, and arcs link angles at the circle to angles at the center.
Here PQ is a tangent at T and TA is a chord. The angle between them is 70°. The tangent meets the radius OT at 90°, so ∠OTA = 90° - 70° = 20°. OT and OA are radii, so triangle OTA is isosceles with base angles of 20°, and the angle at O is 180° - 40° = 140°. Three rules: Tangent and radius, Adjacent angles add, Isosceles triangle.
Challenge
PQ is a tangent to circle O at T, TA is a chord, and the radii OT and OA are drawn. Find ∠TOA, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc11Circle Chases
Tangent Meets ChordTwo Roads to One AngleEnough to Find It?Cyclic Meets IsoscelesRecap: Circle Chases3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles